[FOM] PhD Research Project: Efficient and Natural Proof Systems

Alessio Guglielmi web.alessio.guglielmi at gmail.com
Mon Mar 18 13:42:57 EDT 2013

Hello, could you please help us advertise the 
following position? Ciao,   -Alessio

*** PhD Studentship ***

Research Project: Efficient and Natural Proof Systems

Institution: University of Bath - Department of Computer Science

PhD Supervisors: Alessio Guglielmi and/or Guy McCusker

Application Deadline: 17 April 2013

Math is growing more complex each day, to the 
point that the assistance of computers is 
becoming necessary even for the most 
theoretically inclined among the mathematicians 
(see this recent article by Natalie Wolchover on 
Wired: <http://is.gd/Qf2qpd>). After centuries of 
producing proofs in our heads and then describing 
them in papers, we are moving fast towards a 
future of proofs conceived by humans together 
with computers, which in turn will guarantee 
their correctness and availability.

But what is a proof? What could a common language 
between humans and computers be? A satisfying 
definition of mathematical proof has proved to be 
a very elusive concept. Suffice to say that the 
problem of deciding whether two formal proofs are 
the same has remained open since Hilbert 
formulated it more than one hundred years ago.

Finding efficient and natural proof systems is a 
fascinating problem that spans from philosophy, 
through math, to computer science. There is 
growing evidence that, at its core, good 
solutions can be provided by geometrical ideas. 
Indeed, many mathematicians interested in the 
foundations of mathematics have recently turned 
to geometry.

We propose a PhD in the context of the EPSRC 
project `Efficient and Natural Proof Systems´ 
(see at <http://is.gd/7XYPbt>). In this project, 
we will define a new proof system which, 
essentially, will represent proofs as geometric 
shapes equivalent under continuous deformation. 
Three areas of mathematics and theoretical 
computer science concur in the definition of 
these proof systems: categorical semantics, proof 
theory and proof complexity. The result of this 
project will be the completion of three decades 
of efforts in proof theory that started with 
linear logic and continued with deep inference 
(see <http://is.gd/leM81c> [beware, there are 
jokes in that page]).

We are looking for a brilliant mathematician or 
theoretical computer scientist who is not afraid 
of working with category theory and who has a 
good geometric intuition. We provide a fully 
funded three-year PhD position in the exceptional 
research environment of one of the best worldwide 
research groups in semantics and proof theory 
(see at <http://is.gd/ZUlZ5n>).

Your full tuition fees will be covered and you 
will receive a standard EPSRC maintenance payment 
of £13,726/annum (13/14 rate) for three years. 
Funding for this project is available to citizens 
of a number of European countries (including the 
UK). In most cases this will include all EU 
nationals. However full funding may not be 
available to all applicants and you should read 
the full department and project details for 
further information.

To apply, start here: <http://is.gd/RCaAvA/>. 
Feel free to contact Alessio Guglielmi for any 
question you might have about this position.

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